%% edited by LCP!!  

%%   Commented out the change to \newlinechar

%%   Increased space in Contents

%%   Changed \thebibliography to the defn in llncs.sty

%%   Added ttbox

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%   MATHSING.STY        Version 1.1

%

%   This LaTeX style option file contains necessary macros for writing

%   camera ready English single author math book manuscripts.

%

%

%   Usage:

%

%      \documentstyle[12pt,mathsing]{book}

%        ...

%

%   Change log:

%

%      90/11/04  pagestyle empty for first page of chapter

%      90/11/04  distinct figure and table captions

%      90/11/04  \small for captions and headings

%      90/11/04  improved definition of theorem-like environments

%      90/12/01  separation after chapter title changed to 5.1cm

%      90/12/01  page size changed to 45x14.4+10pt=23.05cm

%      90/12/01  references

%      90/12/01  common counter for theorem-like environments

%      90/12/02  table of contents

%      90/12/02  final improvements and corrections

%      90/12/26  two styles for equation numbers

%      91/02/05  \numberlikebook and \numberlikearticle replace

%                \eqnbook and \eqnarticle

%      91/10/07  \listoffigures, \listoftables made similar to

%                \tableofcontents,

%                running head of Index changed: Sachverzeichnis -> Index,

%                \newthe now uses \thechapter instead of \arabic{chapter}

%      91/02/05  binding: \tablebook, \tablearticle

%                \figurebook, \figurearticle added

%      91/10/07  holzwarth: \listoffigures, \listoftables

%                according to \tableofcontents,

%                \begin{theindex}

%                \newthe to produce correct numbers

%      91/12/03  \chapter, \section, and \subsection now do not

%                hyphenate the headings any more

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%  change the catcode of @ (allows names containing @ after \begin{document})

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\makeatletter

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%     page layout and dimensions

%

% The following commands are redefined:

%

%   \ps@headings    (cf. BOOK.STY)

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%     Layout

%

%     Note: The following values do not apply for English Springer

%     books on phsics; use \baselineskip=14pt, \textwidth=13.8cm,

%     \textheight=640pt (=45x14pt+10pt=22.5cm) instead!

%

\baselineskip=14.4pt          % LaTeX default

\topmargin=0cm

\textwidth=14.2cm             % 1.2 x 11.833 cm

\textheight=658pt             % 45x14.4pt+10pt = 658pt = 23.0554cm

%\textheight=23.2502cm         % 1.2x19.3752cm=23.2502cm (first version)

\oddsidemargin=0.7cm

\evensidemargin=0.7cm

\headsep=20pt                 % ?

\parindent=7mm                % 1.2 x 5.833mm

\hfuzz=2pt                    % supress "overfull box" messages below 2pt

\frenchspacing                % no large blanks at the end of a sentence

\tolerance=500

\abovedisplayskip=3.6 mm plus7.2pt minus 4.8pt

\belowdisplayskip=3.6 mm plus7.2pt minus 4.8pt

\abovedisplayshortskip=0.0 mm plus7.2pt minus 2.4pt

\belowdisplayshortskip=2.4 mm plus4.8pt minus 4.8pt

\predisplaypenalty=0          % penalties for page break

\clubpenalty=10000            %

\widowpenalty=10000           %

%

%     running titles

%

% binding 5.2.91 \hspace changed to 1.0 cm    |           |

% binding 5.2.91 dot deleted after \thesection                 |

\def\ps@headings{

    \let\@mkboth\markboth

    \def\@oddfoot{}

    \def\@evenfoot{}

    \def\@evenhead{\rm\small\thepage\hspace{1.0cm}\leftmark\hfil\hbox{}}

    \def\@oddhead{\hbox{}\hfil\rm\small\rightmark\hspace{1.0cm}\thepage}

    \def\chaptermark##1{\markboth

                        {\ifnum \c@secnumdepth >\m@ne \thechapter.\ \fi ##1}{}}

%hier punkt raus. binding                                      |

    \def\sectionmark##1{\markright

                        {\ifnum \c@secnumdepth >\z@ \thesection\ \fi ##1}}

    }

\pagestyle{headings}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Chapters and Sections

%

% The following commands are redefined:

%

%  \@makechapterhead    (cf. BK12.STY)

%  \@makeschapterhead   (cf. BK12.STY)

%  \chapter             (cf. BK12.STY)

%  \@sect               (cf. LATEX.TEX)

%  \section             (cf. BK12.STY)

%  \subsection          (cf. BK12.STY)

%  \subsubsection       (cf. BK12.STY)

%  \paragraph           (cf. BK12.STY)

%  \subparagraph        (cf. BK12.STY)

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%     number of numbered section levels

%

\setcounter{secnumdepth}{3}

%

%     Adapt the font size for chapter titles and supress printing of

%     the word "chapter"

%

\def\@makechapterhead#1{ { \parindent 0pt \raggedright

% \pretolerance added 12/3/91 fuh

{\pretolerance=10000\Large \bf \thechapter.\hspace{0.3cm}#1\par}%

 \nobreak \vskip 4cm \vskip\baselineskip} }

\def\@makeschapterhead#1{ { \parindent 0pt \raggedright

% \pretolerance added 12/3/91 fuh

 \pretolerance=10000\Large \bf #1\par

 \nobreak \vskip 4cm \vskip\baselineskip} }

%

%     define pagestyle=empty for first page of a chapter

%

\def\chapter{\cleardoublepage \thispagestyle{empty} \global\@topnum\z@

\@afterindentfalse \secdef\@chapter\@schapter}

%

%     Change the distance between section number and title from 1em to 2mm

%     binding:  changed again to 1en=0.5em       |     5.2.91

%

\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth

     \def\@svsec{}\else

     \refstepcounter{#1}%

     \edef\@svsec{\csname the#1\endcsname\hskip 0.5em }\fi

     \@tempskipa #5\relax

      \ifdim \@tempskipa>\z@

        \begingroup #6\relax

% changed by Binding :) 20.3.91

% old:    \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}

% \@hangfrom deleted to avoid hanging indentation \noindent added

          {\noindent\hskip #3\relax\@svsec}%

          {\interlinepenalty \@M #8\par}

        \endgroup

       \csname #1mark\endcsname{#7}\addcontentsline

         {toc}{#1}{\ifnum #2>\c@secnumdepth \else

                      \protect\numberline{\csname the#1\endcsname}\fi

                    #7}\else

        \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname

                      {#7}\addcontentsline

                           {toc}{#1}{\ifnum #2>\c@secnumdepth \else

                             \protect\numberline{\csname the#1\endcsname}\fi

                       #7}}\fi

     \@xsect{#5}}

%

%     Font size for section titles;

%     Increased vertical space before and after sections, subsections

%     and subsubsections by 1ex; run-in headings starting with subsubsection

%

%     (\@startsection{NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE})

%

%binding, 18.3.91:  \boldmath inserted

\def\section{\@startsection{section}{1}{\z@}{

             -4.50ex plus -1ex minus -.2ex}{3.3ex plus .2ex}

             {\large\bf\boldmath\raggedright\pretolerance=10000}}

% \raggedright and \pretolerance added 12/3/91 fuh

\def\subsection{\@startsection{subsection}{2}{\z@}{

             -4.25ex plus -1ex minus -.2ex}{2.5ex plus .2ex}

             {\normalsize\bf\boldmath\raggedright\pretolerance=10000}}

% \raggedright and \pretolerance added 12/3/91 fuh

\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{

             -3.25ex plus -1ex minus -.2ex}{-0.5em}

             {\normalsize\bf\boldmath}}

\def\paragraph{\@startsection{paragraph}{4}{\z@}{

             -3.25ex plus -1ex minus -.2ex}{-0.5em}{\normalsize\it}}

\def\subparagraph{\@startsection{subparagraph}{5}{\@}{

             -3.25ex plus -1ex minus -.2ex}{-0.5em}{\normalsize\it}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%20.3.91, binding: \labelitemi changed

\renewcommand{\labelitemi}{$\bullet$}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Tables

%

% Change width of horizontal and vertical lines in arrays and tables

%

% The following commands are redefined:

%

%  \arrayrulewidth

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\arrayrulewidth0.15mm

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Figure and table captions (small)

%

% To meet the different requirements for table and figure captions

% new macros \@makefigurecaption and \@maketablecaption are introduced

% in addition to \@makecaption (cf. BOOK.STY). The \@caption macro is

% changed to check for figures and tables.

%

% The following commands are redefined:

%

%  \@caption         (cf. LATEX.TEX)

%  \fnum@figure      (cf. BOOK.STY)

%  \fnum@table       (cf. BOOK.STY)

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\long\def\@caption#1[#2]#3{\addcontentsline{\csname

  ext@#1\endcsname}{#1}{\protect\numberline{\csname

  the#1\endcsname}{\ignorespaces #2}}\par

  \begingroup

    \@parboxrestore

    \normalsize

    \csname @make#1caption\endcsname

    {\csname fnum@#1\endcsname}{\ignorespaces #3}\par

  \endgroup}

\long\def\@makefigurecaption#1#2{

 \vskip 10pt                     % skip between figure and caption

 {\small                         % required here for correct \baselineskip !

 \setbox\@tempboxa\hbox{\small{\bf#1}#2}

 \ifdim \wd\@tempboxa >\hsize

   \unhbox\@tempboxa\par

 \else

   \hbox to\hsize{\hfil\box\@tempboxa\hfil}       % centered short caption !

 \fi}

 \vskip 10pt}                    % additional space between caption and text

\long\def\@maketablecaption#1#2{

 \vskip 10pt                     % additional space between text and caption

 {\small                         % required here for correct \baselineskip !

 \setbox\@tempboxa\hbox{\small{\bf#1}#2}

 \ifdim \wd\@tempboxa >\hsize

   \unhbox\@tempboxa\par

 \else \hbox  to\hsize{\box\@tempboxa\hfil}   % leftadjusted short caption !

 \fi}

 \vskip 10pt}                    % skip between caption and table

\def\fnum@figure{Fig.$\,$\thefigure.$\;$}

\def\fnum@table{Table$\,$\thetable.$\;$}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%  Distance between text and floatings (tables, figures)

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\floatsep 14pt plus 2pt minus 4pt        % LaTeX defaults values

\textfloatsep 20pt plus 2pt minus 4pt    %

\intextsep 14pt plus 4pt minus 4pt       %

\@maxsep 20pt                            %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Table of contents

%

% The following commands are redefined:

%

%  \l@chapter        (cf. LATEX.STY)

%  \tableofcontents

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%     lowest level for table of contents entries

%

\setcounter{tocdepth}{3}

%

%     dotted line for chapters in table of contents

%     (cf. definition of \@dottedline in LATEX.STY)

%

\def\l@chapter#1#2{\pagebreak[3]

 \vskip 1.0em plus 1pt \@tempdima 1.5em \begingroup

 \parindent \z@ \rightskip \@pnumwidth

 \parfillskip -\@pnumwidth

 \rm \leavevmode #1

 \nobreak\leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern \@dotsep mu$}\hfill

 \nobreak

 \hbox to\@pnumwidth{\hss \rm #2}\par

 \endgroup}

%copied from book.sty to leave room for 12.11, etc. -- Frank Holzwarth via LCP

\def\l@section{\@dottedtocline{1}{1.5em}{2.8em}}

%

%     Adaption of \tableofcontents (title,headings,pagenumber)

%

\def\tableofcontents{

     \@restonecolfalse

     \if@twocolumn\@restonecoltrue\onecolumn\fi

     \chapter*{Table of Contents}

     \markboth{Table of Contents}{Table of Contents}  % headline

     \renewcommand{\thepage}{\Roman{page}}            % roman page number

     \@starttoc{toc}\if@restonecol\twocolumn\fi}

%%%%%%%% added 91/10/07 fuh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% List of figures

%

% The following commands are redefined:

%

%  \listoffigures

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

\def\listoffigures{

     \@restonecolfalse

     \if@twocolumn\@restonecoltrue\onecolumn\fi

     \chapter*{List of Figures}

     \markboth{List of Figures}{List of Figures}      % headline

     \renewcommand{\thepage}{\Roman{page}}            % roman page number

     \@starttoc{lof}\if@restonecol\twocolumn\fi}

%%%%%%%% added 91/10/07 fuh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% List of tables

%

% The following commands are redefined:

%

%  \listoftables

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

\def\listoftables{

     \@restonecolfalse

     \if@twocolumn\@restonecoltrue\onecolumn\fi

     \chapter*{List of Tables}

     \markboth{List of Tables}{List of Tables}        % headline

     \renewcommand{\thepage}{\Roman{page}}            % roman page number

     \@starttoc{lot}\if@restonecol\twocolumn\fi}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Index (with table of contents entry)

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\theindex{ \cleardoublepage

               \small

               \columnseprule \z@

               \columnsep=0.84cm

               \twocolumn[\@makeschapterhead{Index}]

               \addcontentsline{toc}{chapter}{Index}

               \@mkboth{Index}{Index}

               \thispagestyle{plain}\parindent\z@

               \parskip\z@ plus .3pt\relax\let\item\@idxitem}

\def\@idxitem{\par\hangindent 15pt}

\def\subitem{\par\hangindent 15pt -- }

\def\endtheindex{\clearpage}

\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% References (Bibliography)

%

% Macros for creating a list of references in small print using LaTeX

% defaults or some special Springer commands.

%

% Usage:

%

%   \begin{thebibliography}{wide-label}      % LaTeX standard macros

%     \bibitem[label]{name} ... text ...

%     \bibitem[label]{name} ... text ...

%   \end{thebibliography}

%

%   or

%

%   \begin{references}{wide-label}           % Springer macros

%     \refer            ... text ...

%     \refno{no.}       ... text ...

%     \refmark{[label]} ... text ...

%   \end{references}

%

% New commands:

%

%   \refchapter      starts an unnumbered chapter "References"; small font

%   \refer           unlabeled item with hanging indentation

%   \refno           right adjusted label (for numbers)

%   \refmark         left adjusted label (for text labels)

%

% Changed commands

%

%   \thebibliography       (BOOK.STY)   (further edit by LCP!)

%   \endthebibliography    (BOOK.STY)

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\refchapter{\chapter*{References}

\parindent0pt\parskip0pt\small

\addcontentsline{toc}{chapter}{References}

\markboth{References}{References}}

\def\thebibliography#1{\refchapter\small\list

  {\arabic{enumi}.}{\settowidth\labelwidth{#1.}\leftmargin\labelwidth

    \advance\leftmargin\labelsep

    \usecounter{enumi}}

    \def\newblock{\hskip .11em plus .33em minus -.07em}

    \sloppy

    \sfcode`\.=1000\relax}

\let\endthebibliography=\endlist

\newenvironment{references}[1]{\refchapter

                               \settowidth\labelwidth{#1\enspace}

                               \begingroup}{\endgraf\endgroup}

%

% The following macros are from REFER.TEX.

% \refindent is replaced by the predefined dimension \labelwidth

% that is also used by \thebibliography; \ref is replaced by \refer

% since \ref is already used for referencing lables!

%%%\newlinechar=`\|

% \refer produces ordinary entries, successive line are indented 1em

\def\refer{\goodbreak\hangindent1em\hangafter=1\noindent\ignorespaces}

% \refno produces entries with right-aligned marks in the margin

\def\refno#1{\goodbreak

\setbox0=\hbox{#1\enspace}\ifdim\labelwidth<\wd0\relax

\message{|Your reference `#1' is wider than you pretended in using

\string\begref.}\fi

\hangindent\labelwidth\hangafter=1\noindent

\kern\labelwidth\llap{#1\enspace}\ignorespaces}

% \refmark produces entries with left-aligned marks in the margin

\def\refmark#1{\goodbreak

\setbox0=\hbox{#1\enspace}\ifdim\labelwidth<\wd0\relax

\message{|Your reference `#1' is wider than you pretended in using

\string\begref.}\fi

\hangindent\labelwidth\hangafter=1\noindent

\hbox to\labelwidth{#1\hss}\ignorespaces}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%  New environments

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%  The following lines define a new environment 'listing'

%

%         \begin{listing}

%               ...

%         \end{listing}

%

%  that prints listings using \footnotesize and takes care to reset

%  the \baselineskip. The macro definition is based on ALLTT.STY that

%  allows various TEX commands to be given within the environment

%  (e.g. '\input', '\index' or '\it'). '%' has been retained as a special

%  character within 'listing', however, to avoid unwanted line breaks.

%

%

\def\docspecials{\do\ \do\$\do\&%

  \do\#\do\^\do\^^K\do\_\do\^^A\do\~}

\newdimen\oldbaselineskip

\def\listing{\par\noindent\oldbaselineskip=\baselineskip \footnotesize%

\trivlist \item[]\if@minipage\else\vskip\parskip\fi

\leftskip\@totalleftmargin\rightskip\z@

\parindent\z@\parfillskip\@flushglue\parskip\z@

\@tempswafalse \def\par{\if@tempswa\hbox{}\fi\@tempswatrue\@@par}

\obeylines \tt \catcode``=13 \@noligs \let\do\@makeother \docspecials

 \frenchspacing\@vobeyspaces}

\def\endlisting{\endtrivlist\baselineskip=\oldbaselineskip}

%Add ttbox to Springer's macros!!  - LCP

\newenvironment{ttbox}{\par\nobreak\vskip-2pt%

           \vbox\bgroup\begin{listing}\leftskip\leftmargini}%

        {\end{listing}\egroup\vskip-7pt\@endparenv}

\newcommand\ttbreak{\end{ttbox}\goodbreak\vskip-8pt plus 3pt\begin{ttbox}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Acknowledgements ( = acknow.tex)

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\ack#1{\vskip11pt\begingroup\noindent{\it Acknowledgements\/}.

\ignorespaces#1\vskip6pt\endgroup}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Definition of versal greek letters ( = ucgreek.tex)

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\mathchardef\Gamma="0100

\mathchardef\Delta="0101

\mathchardef\Theta="0102

\mathchardef\Lambda="0103

\mathchardef\Xi="0104

\mathchardef\Pi="0105

\mathchardef\Sigma="0106

\mathchardef\Upsilon="0107

\mathchardef\Phi="0108

\mathchardef\Psi="0109

\mathchardef\Omega="010A

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Vectors ( = vector.tex)

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% This is vector.tex

% it redefines the plain TeX \vec command

% to produce bold characters

%

\def\vec#1{\ifmmode

\mathchoice{\mbox{\boldmath$\displaystyle\bf#1$}}

{\mbox{\boldmath$\textstyle\bf#1$}}

{\mbox{\boldmath$\scriptstyle\bf#1$}}

{\mbox{\boldmath$\scriptscriptstyle\bf#1$}}\else

{\mbox{\boldmath$\bf#1$}}\fi}

%

%\def\vec#1{{\textfont0=\tenbf\scriptfont0=\sevenbf

%\scriptscriptfont0=\fivebf

%\textfont1=\tenbf\scriptfont1=\sevenbf

%\scriptscriptfont1=\fivebf

%\ifmmode % supply all varieties of math sizes

%   \mathchoice{\hbox{$\displaystyle#1$}}{\hbox{$\textstyle#1$}}

%   {\hbox{$\scriptstyle#1$}}{\hbox{$\scriptscriptstyle#1$}}

%\else\hbox{$#1$}\fi}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% Symbols ( = symbols.tex )

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% This is symbols.tex

% the symbols not available in plain TeX are constructed

% by overprinting some characters

\def\sun{{\hbox{$\odot$}}}

\def\la{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.5pt}\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr

\noalign{\vskip1.0pt}\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr

\noalign{\vskip0.5pt}\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil

\cr<\cr\noalign{\vskip0.5pt}\sim\cr}}}}}

\def\ga{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.5pt}\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr

\noalign{\vskip1.0pt}\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr

\noalign{\vskip0.5pt}\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil

\cr>\cr\noalign{\vskip0.5pt}\sim\cr}}}}}

\def\sq{\hbox{\rlap{$\sqcap$}$\sqcup$}}

\def\degr{\hbox{$^\circ$}}

\def\arcmin{\hbox{$^\prime$}}

\def\arcsec{\hbox{$^{\prime\prime}$}}

\def\utw{\smash{\rlap{\lower5pt\hbox{$\sim$}}}}

\def\udtw{\smash{\rlap{\lower6pt\hbox{$\approx$}}}}

\def\fd{\hbox{$.\!\!^{\rm d}$}}

\def\fh{\hbox{$.\!\!^{\rm h}$}}

\def\fm{\hbox{$.\!\!^{\rm m}$}}

\def\fs{\hbox{$.\!\!^{\rm s}$}}

\def\fdg{\hbox{$.\!\!^\circ$}}

\def\farcm{\hbox{$.\mkern-4mu^\prime$}}

\def\farcs{\hbox{$.\!\!^{\prime\prime}$}}

\def\fp{\hbox{$.\!\!^{\scriptscriptstyle\rm p}$}}

\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip

\halign{\hfil$\displaystyle##$\hfil\cr\gets\cr\to\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr

\gets\cr\to\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr

\gets\cr\to\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr

\gets\cr\to\cr}}}}}

\def\cor{\mathrel{\mathchoice {\hbox{$\widehat=$}}{\hbox{$\widehat=$}}

{\hbox{$\scriptstyle\hat=$}}

{\hbox{$\scriptscriptstyle\hat=$}}}}

\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1.5pt}<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr

>\cr\noalign{\vskip-1.5pt}<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr

>\cr\noalign{\vskip-1pt}<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr

>\cr\noalign{\vskip-0.5pt}<\cr}}}}}

\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.5pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr

\noalign{\vskip1pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr

\noalign{\vskip0.5pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr

<\cr\noalign{\vskip0.5pt}=\cr}}}}}

\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.5pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr

\noalign{\vskip1pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr

\noalign{\vskip0.5pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr

>\cr\noalign{\vskip0.5pt}=\cr}}}}}

\def\sol{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr\sim\cr\noalign{\vskip-0.2mm}<\cr}}}

{\vcenter{\offinterlineskip

\halign{\hfil$\textstyle##$\hfil\cr\sim\cr<\cr}}}

{\vcenter{\offinterlineskip

\halign{\hfil$\scriptstyle##$\hfil\cr\sim\cr<\cr}}}

{\vcenter{\offinterlineskip

\halign{\hfil$\scriptscriptstyle##$\hfil\cr\sim\cr<\cr}}}}}

\def\sog{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr\sim\cr\noalign{\vskip-0.2mm}>\cr}}}

{\vcenter{\offinterlineskip

\halign{\hfil$\textstyle##$\hfil\cr\sim\cr>\cr}}}

{\vcenter{\offinterlineskip

\halign{\hfil$\scriptstyle##$\hfil\cr\sim\cr>\cr}}}

{\vcenter{\offinterlineskip

\halign{\hfil$\scriptscriptstyle##$\hfil\cr\sim\cr>\cr}}}}}

\def\lse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.5pt}\simeq\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr

\noalign{\vskip1pt}\simeq\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr

\noalign{\vskip0.5pt}\simeq\cr}}}

{\vcenter{\offinterlineskip

\halign{\hfil$\scriptscriptstyle##$\hfil\cr<\cr

\noalign{\vskip0.5pt}\simeq\cr}}}}}

\def\gse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.5pt}\simeq\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr

\noalign{\vskip1.0pt}\simeq\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr

\noalign{\vskip0.5pt}\simeq\cr}}}

{\vcenter{\offinterlineskip

\halign{\hfil$\scriptscriptstyle##$\hfil\cr>\cr

\noalign{\vskip0.5pt}\simeq\cr}}}}}

\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1.5pt}<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr

>\cr\noalign{\vskip-1.5pt}<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr

>\cr\noalign{\vskip-1pt}<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr

>\cr\noalign{\vskip-0.5pt}<\cr}}}}}

\def\leogr{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr<\cr\noalign{\vskip-1.5pt}>\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr

<\cr\noalign{\vskip-1.5pt}>\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr

<\cr\noalign{\vskip-1pt}>\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr

<\cr\noalign{\vskip-0.5pt}>\cr}}}}}

\def\loa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.5pt}\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr

\noalign{\vskip1.0pt}\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr

\noalign{\vskip0.5pt}\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr

<\cr\noalign{\vskip0.5pt}\approx\cr}}}}}

\def\goa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.5pt}\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr

\noalign{\vskip1.0pt}\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr

\noalign{\vskip0.5pt}\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr

>\cr\noalign{\vskip0.5pt}\approx\cr}}}}}

\def\bbbr{{\rm I\!R}} %reelle Zahlen

\def\bbbn{{\rm I\!N}} %natuerliche Zahlen

\def\bbbm{{\rm I\!M}}

\def\bbbh{{\rm I\!H}}

\def\bbbf{{\rm I\!F}}

\def\bbbk{{\rm I\!K}}

\def\bbbp{{\rm I\!P}}

\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l}

{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}}

\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox

to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}

{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox

to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}

{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox

to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}

{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox

to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}}

\def\bbbe{{\mathchoice {\setbox0=\hbox{\smalletextfont e}\hbox{\raise

0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.3pt

height0.7\ht0\hss}\box0}}

{\setbox0=\hbox{\smalletextfont e}\hbox{\raise

0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.3pt

height0.7\ht0\hss}\box0}}

{\setbox0=\hbox{\smallescriptfont e}\hbox{\raise

0.1\ht0\hbox to0pt{\kern0.5\wd0\vrule width0.2pt

height0.7\ht0\hss}\box0}}

{\setbox0=\hbox{\smallescriptscriptfont e}\hbox{\raise

0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.2pt

height0.7\ht0\hss}\box0}}}}

\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm Q$}\hbox{\raise

0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}

{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise

0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}

{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise

0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}

{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise

0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}}

\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm

T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}

{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox

to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}

{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox

to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}

{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox

to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}}

\def\bbbs{{\mathchoice

{\setbox0=\hbox{$\displaystyle     \rm S$}\hbox{\raise0.5\ht0\hbox

to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox

to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}

{\setbox0=\hbox{$\textstyle        \rm S$}\hbox{\raise0.5\ht0\hbox

to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox

to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}

{\setbox0=\hbox{$\scriptstyle      \rm S$}\hbox{\raise0.5\ht0\hbox

to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox

to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}}

{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox

to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox

to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}}

%

% note: changed \sans to \sf for LaTeX

%

\def\bbbz{{\mathchoice {\hbox{$\sf\textstyle Z\kern-0.4em Z$}}

{\hbox{$\sf\textstyle Z\kern-0.4em Z$}}

{\hbox{$\sf\scriptstyle Z\kern-0.3em Z$}}

{\hbox{$\sf\scriptscriptstyle Z\kern-0.2em Z$}}}}

\def\diameter{{\ifmmode\oslash\else$\oslash$\fi}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% petit  (substitute for petit.tex)

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newenvironment{petit}{\vskip6pt\begingroup\small}{\endgroup\vskip6pt}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% New environments

%

%   lemma, proposition, theorem, corollary  (\bf,\it)  (numbered)

%   exercise, problem, solution, definition (\bf,\rm)

% 27.3.91 binding: example, note and question changed to (\bf, \rm)

%

%   lemma*, proposition*, theorem*, corollary*  (\bf,\it)   (unnumbered)

%   exercise*, problem*, solution*, definition* (\bf,\rm)

%   example*, note*, question* (\it,\rm)

%

%   remark, proof (\it,\rm)  (unnumbered)

%

%   usage:   \begin{lemma}  or  \begin{lemma}[COMMENT]

%              ...                ...

%            \end{lemma}        \end{lemma}

%

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% currently one counter is used for all theorem like environments

\newcounter{lemmacount}[chapter]

\renewcommand{\thelemmacount}{\thechapter.\arabic{lemmacount}}

%

% short form for defininng new theorem like environments:

% \newthe{NAME}{NAME*}{TITLE}{COUNTER}{FONT1}{FONT2}

%

\def\@@begthe#1{\@ifnextchar[{\@optbegthe#1}{\@begthe#1}}

%27.3.91 binding: dot deleted

%def\@begthe#1{. #1}   old

\def\@begthe#1{ #1}

\def\@optbegthe#1[#2]{ {#2} #1}

\newcommand{\newthe}[6]{

 \def\nlni{\par\ifvmode\removelastskip\fi\vskip\baselineskip\noindent}

 \def\xxxend{\endgroup\vskip\baselineskip}

 \newenvironment{#1}{\nlni\begingroup\refstepcounter{#4}#5#3

%changed 91/10/7 fuh:\arabic{chapter}.\arabic{#4}\@@begthe{#6}}{\xxxend}

                     \thechapter.\arabic{#4}\@@begthe{#6}}{\xxxend}

 \newenvironment{#2}{\nlni\begingroup#5#3\@@begthe{#6}}{\xxxend}}

% Lemma, Proposition, Theorem, Corollary  (\bf,\it)

\newthe{lemma}{lemma*}{Lemma}{lemmacount}{\bf}{\it}

\newthe{proposition}{proposition*}{Proposition}{lemmacount}{\bf}{\it}

\newthe{theorem}{theorem*}{Theorem}{lemmacount}{\bf}{\it}

\newthe{corollary}{corollary*}{Corollary}{lemmacount}{\bf}{\it}

% Exercise, Problem, Solution, Definition (\bf,\rm)

\newthe{exercise}{exercise*}{exercise}{lemmacount}{\bf}{\it}

\newthe{problem}{problem*}{Problem}{lemmacount}{\bf}{\it}

\newthe{solution}{solution*}{Solution}{lemmacount}{\bf}{\it}

\newthe{definition}{definition*}{Definition}{lemmacount}{\bf}{\it}

% Example, Note, Question (\bf,\rm)

\newthe{example}{example*}{Example}{lemmacount}{\bf}{\rm}

\newthe{note}{note*}{Note}{lemmacount}{\bf}{\rm}

\newthe{question}{question*}{Question}{lemmacount}{\bf}{\rm}

% Remark, Proof

\newenvironment{remark}{\nlni\begingroup\it Remark. \rm}{

                        \endgroup\vskip\baselineskip}

\newenvironment{proof}{\nlni\begingroup\it Proof. \rm}{

                       \endgroup\vskip\baselineskip}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

% qed

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\qed{\ifmmode\sq\else{\unskip\nobreak\hfil

\penalty50\hskip1em\null\nobreak\hfil\sq

\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%  \eqnarticle    simple equation numbers without chapter number

%  \eqnbook       structured equation numbers (default)

%   changed by binding 5.2.91: changed to \numberlikearticle and

%                                \numberlikebook, changing numbering of

%                              figures and tables also.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\numberlikearticle{\global\def\theequation{\arabic{equation}}

\global\def\thetable{\arabic{table}}

\global\def\thefigure{\arabic{figure}}}

\def\numberlikebook{\global\def\theequation{\thechapter.\arabic{equation}}

\global\def\thetable{\thechapter.\arabic{table}}

\global\def\thefigure{\thechapter.\arabic{figure}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%  Redeclaration of \makeatletter; no @-expressions may be used from now on

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\makeatother

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%

%   End of MATHSING.STY

%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%